My Math Forum what is: sin(a+b)/sin(a-b)

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 September 12th, 2018, 11:24 AM #1 Member   Joined: Jul 2018 From: Germany Posts: 32 Thanks: 1 what is: sin(a+b)/sin(a-b) is there any simpler way to write this, I already looked at all the trigonometric identities, I couldn't find anything about fractions of sums. I also try to find: cos(a-b)+cos(a+b) how do I do this, is there anything I'm missing?
 September 12th, 2018, 02:01 PM #2 Global Moderator   Joined: May 2007 Posts: 6,628 Thanks: 622 You can always write x=a+b and y=a-b., get sin(x)/sin(y) or cps(y)/cos(x). You can't do anything more, since the angles are completely arbitrary. Thanks from theHeavyLobster
 September 12th, 2018, 09:23 PM #3 Global Moderator   Joined: Dec 2006 Posts: 19,887 Thanks: 1836 sin(a + b) $\ \$ tan(a) + tan(b) --------- = --------------- sin(a - b) $\ \$ tan(a) - tan(b) cos(A - B) + cos(A + B) ≡ 2cos(A)cos(B) Thanks from theHeavyLobster
September 13th, 2018, 05:14 AM   #4
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Quote:
 Originally Posted by mathman since the angles are completely arbitrary.

a = $\displaystyle \epsilon + \alpha$
b = $\displaystyle \epsilon$

September 13th, 2018, 05:16 AM   #5
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Quote:
 Originally Posted by skipjack sin(a + b) $\ \$ tan(a) + tan(b) --------- = --------------- sin(a - b) $\ \$ tan(a) - tan(b) cos(A - B) + cos(A + B) ≡ 2cos(A)cos(B)

That's nice, thank you!

September 13th, 2018, 02:39 PM   #6
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Quote:
 Originally Posted by theHeavyLobster Hold on, I forgot about this: a = $\displaystyle \epsilon + \alpha$ b = $\displaystyle \epsilon$
Are $\alpha$ and $\epsilon$ related? If not, you have a simple change of variables with no more information.

September 14th, 2018, 03:08 PM   #7
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Quote:
 Originally Posted by mathman Are $\alpha$ and $\epsilon$ related? If not, you have a simple change of variables with no more information.
Ah, yeah you're right. No alpha and epsilon are unrelated.

 Tags b or sinab, cos, fraction, simplify, sin, sina

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